A 400V dc. motor develops a shaft torque of 150Nm at 3000 rev/min. If the efficiency is83%, determine the current supplied to the motor.

To solve this problem, we need to follow these steps:

Step 1: Convert the speed from revolutions per minute (rev/min) to radians per second (rad/s) because the SI unit of speed is rad/s. We know that 1 rev = 2π rad and 1 min = 60 s. So, 3000 rev/min = 3000 * 2π / 60 = 100π rad/s.

Step 2: Calculate the power developed at the shaft using the formula: Power = Torque * Speed. Substituting the given values, we get Power = 150 Nm * 100π rad/s = 15000π Watts.

Step 3: Calculate the input power to the motor. We know that Efficiency = Output Power / Input Power. Rearranging, we get Input Power = Output Power / Efficiency = 15000π / 0.83 ≈ 18000π Watts.

Step 4: Calculate the current supplied to the motor using the formula: Power = Voltage * Current. Rearranging, we get Current = Power / Voltage = 18000π / 400 ≈ 45π Amperes.

So, the current supplied to the motor is approximately 45π Amperes.